Module 2
What is Number System ?
A number system is a way to represent and express numbers
using a consistent set of symbols or digits.
•A number system uses a base (or radix) to represent values.
Most commonly used number systems are Decimal (base-
10), Binary (base-2), Octal (base-8), and Hexadecimal (base-16).
Each system has its own set of rules for representing.
•Digital systems primarily rely on the Binary system for data
processing.
Types of Number System
There are four common types of number systems based on the radix or
base of the number :
Decimal Number System
•The Decimal system is a base-10 number system.
•It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
•Each digit’s place value is a power of 10 (e.g., 100, 101, 102).
•It is the standard system for everyday counting and calculations.
Binary Number System
•The Binary system is a base-2 number system.
•It uses two digits: 0 and 1.
•Each digit’s place value is a power of 2 (e.g., 20, 21, 22).
•The Binary system is the foundation for data representation in computers
and digital electronics.
, Octal Number System
•The Octal system is a base-8 number system.
•It uses eight digits: 0, 1, 2, 3, 4, 5, 6 and 7.
•Each digit’s place value is a power of 8 (e.g., 80, 81, 82).
•It is often used to simplify the representation of binary numbers by
grouping them into sets of three bits.
Hexadecimal Number System
•The Hexadecimal system is a base-16 number system.
•It uses sixteen digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F (where A =
10, B = 11, etc.).
•Each digit’s place value is a power of 16 (e.g., 160, 161, 162).
•Hexadecimal simplifies binary by representing every 4 bits as one digit (0-
F).
What is Number System ?
A number system is a way to represent and express numbers
using a consistent set of symbols or digits.
•A number system uses a base (or radix) to represent values.
Most commonly used number systems are Decimal (base-
10), Binary (base-2), Octal (base-8), and Hexadecimal (base-16).
Each system has its own set of rules for representing.
•Digital systems primarily rely on the Binary system for data
processing.
Types of Number System
There are four common types of number systems based on the radix or
base of the number :
Decimal Number System
•The Decimal system is a base-10 number system.
•It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
•Each digit’s place value is a power of 10 (e.g., 100, 101, 102).
•It is the standard system for everyday counting and calculations.
Binary Number System
•The Binary system is a base-2 number system.
•It uses two digits: 0 and 1.
•Each digit’s place value is a power of 2 (e.g., 20, 21, 22).
•The Binary system is the foundation for data representation in computers
and digital electronics.
, Octal Number System
•The Octal system is a base-8 number system.
•It uses eight digits: 0, 1, 2, 3, 4, 5, 6 and 7.
•Each digit’s place value is a power of 8 (e.g., 80, 81, 82).
•It is often used to simplify the representation of binary numbers by
grouping them into sets of three bits.
Hexadecimal Number System
•The Hexadecimal system is a base-16 number system.
•It uses sixteen digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F (where A =
10, B = 11, etc.).
•Each digit’s place value is a power of 16 (e.g., 160, 161, 162).
•Hexadecimal simplifies binary by representing every 4 bits as one digit (0-
F).
